A035453 - OEIS

%I #13 Aug 04 2020 08:45:13

%S 1,1,1,1,1,1,2,2,3,3,3,3,3,4,5,6,7,8,8,8,9,10,12,14,16,17,18,19,20,23,

%T 26,30,33,36,38,40,43,47,53,59,65,70,74,78,84,92,101,112,122,131,139,

%U 147,157,170,186,203,220,235,249,264,281,303,329,357,384,410,434,459

%N Number of partitions of n into parts 8k+1 or 8k+7.

%H Robert Price, <a href="/A035453/b035453.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ (3+2*sqrt(2))^(1/4) * exp(Pi*sqrt(n/6)) / (4 * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 26 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(1 - x^(8k+7))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)

%t nmax = 60; kmax = nmax/8;

%t s = Flatten[{Range[0, kmax]*8 + 1}~Join~{Range[0, kmax]*8 + 7}];

%t Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 03 2020 *)

%Y Cf. A035684.

%K nonn

%O 1,7

%A _Olivier Gérard_